In this work, MILP formulations for a packed bed sensible thermal energy storage for the integration in a UC-framework are presented, taking into account the storage temperature. First, a model for power and temperature from previous work is extended to describe the maximum available power and the storage temperature more precisely. Second, a formulation is presented that satisfies a minimum temperature requirement at the process demand side by mixing the storage mass flow with hot mass flow from a generating unit, if necessary. Third, an approximation of the storage saturation losses during the charging process is presented. All proposed formulations are compared by simulations with receding horizon with feedback of an accurate simulation model. The results show that the minimum temperature requirement can be adhered with the corresponding formulation and the consideration of saturation losses has a significant impact on the system performance and should not be neglected. (C) 2019 Elsevier Ltd. All rights reserved.